Great disnub cube

Great disnub cube
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidsac
Elements
Components	6 square antiprisms
Faces	48 triangles, 12 squares as 6 stellated octagons
Edges	48+48
Vertices	48
Vertex figure	Isosceles trapezoid, edge length 1, 1, 1, √2
Measures (edge length 1)
Circumradius	$\sqrt{\frac{4+\sqrt2}{8}} \approx 0.82267$
Volume	$2\sqrt{4+3\sqrt2} \approx 5.74200$
Dihedral angles	3–3: $\arccos\left(\frac{1-2\sqrt2}{3}\right) \approx 127.55160^\circ$
	4–3: $\arccos\left(\frac{\sqrt3-\sqrt6}{3}\right) \approx 103.83616^\circ$
Central density	6
Number of external pieces	336
Level of complexity	52
Related polytopes
Army	Semi-uniform Girco
Regiment	Gidsac
Dual	Compound of six square antitegums
Conjugate	Great disnub cube
Abstract & topological properties
Flag count	384
Orientable	Yes
Properties
Symmetry	B3, order 48
Convex	No
Nature	Tame

The great disnub cube, gidsac, or compound of six square antiprisms is a uniform polyhedron compound. It consists of 48 triangles and 12 squares (which pair up into 6 stellated octagons due to lying in the same plane), with one square and three triangles joining at a vertex.

It can be formed by combining the two chiral forms of the great snub cube.

Its quotient prismatic equivalent is the square antiprismatic hexateroorthowedge, which is eight-dimensional.

Vertex coordinates

The vertices of a great disnub cube of edge length 1 are given by all permutations of:

• $\left(\pm\sqrt{\frac{2+\sqrt2}{8}},\,\pm\sqrt{\frac{2-\sqrt2}{8}},\,\pm\frac{\sqrt[4]{8}}{4}\right).$

External links

• Bowers, Jonathan. "Polyhedron Category C8: Antiprismatics" (#47).

• Klitzing, Richard. "gidsac".

• Wikipedia Contributors. "Compound of six square antiprisms".